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So it turns out that if someone says that classical music is beautiful and heavenly, they aren't expressing their opinion...that person is stating a fact. I have to give a little background info before I explain.

A few years ago I heard about a phenomenon called "The Divine Proportion", also known as the Golden Section, the Golden Ratio, Phi, and a few others. For those who are new to this ratio, it is 1.61803399:1 and is everpresent in nature. This is the number of female bees to every male bee you will find in any hive in the world. The number of petals in relation to the number of leaves on a flower. It is the basis on which a person's beauty is measured - the closer one's face fits this ratio, the more attractive they are. The list goes on, but I want to get to the point.

Turns out, classical music is littered with this ratio. One of the most fascinating examples I discovered is in Mozart's first sonata. His first movement is 100 measures. The exposition is 38 measures. The recapitulation and development section contains 62 measures. In a 100-measure movement, you cannot attain a closer ratio to the Divine Proportion. Apparently other composers such as Beethoven and Dvorak also toyed with this ratio as well. This floored me upon discovery and I wanted to share it with those who were unaware of its presence. Personally, I can't wait to stop those who try to convince me of Green Day's superiority to Mozart or Beethoven in their tracks by busting out this little nugget of information.

A clear answer to Putz's question required looking at more than one sonata. So Putz examined 29 movements from Mozart's piano sonatas-the ones that consist of two distinct sections. Then he plotted the number of measures in the development and recapitulation versus the total number of measures in each movement, which is the right side of the golden--section equality as given earlier. The results reveal a stunningly straight line-so straight that its correlation coefficient equals 0.99, or nearly the 1.00 of a perfectly straight line. Moreover, the distribution of the ratios of the number of measures in the development and recapitulation to the total number of measures in each movement lies tightly packed and virtually on top of the golden ratio.

Although those results might seem like solid evidence that Mozart did use the golden ratio when he divided the sections of his piano sonatas, Putz knew that another comparison must be made. If Mozart used the golden section, then the other ratio from the golden--section equality--in this case, the ratio of the number of measures in an exposition to those in the recapitulation and development--should also equal the golden ratio. A plot of those measurements also produces a very straight line, but one with a lower correlation coefficient of 0.938, which Putz interpreted as "somewhat less goodness of fit." In addition, the distribution of the ratios of the number of measures in the expositions to those in the recapitulation and development peaks near the golden ratio of 0.618, but it also covers a considerable spread, ranging from 0.534 to 0.833.

The results from the two analyses seemingly conflict. The first analysis suggests that Mozart probably did use the golden section, but the variability in the ratios from the second analysis suggests that he did not use the golden section. That disagreement, however, did not surprise Putz, who wrote that the mathematics behind the golden section predict that "what we have observed in these data is true for all data...." That is, the ratio of the longer segment to the overall length is always closer to the golden ratio than is the ratio of the shorter segment to the longer one. As such, Putz concentrated on the distribution of the latter ratio as constrained by sonata form, and the spread in the distribution of ratios from that analysis suggests that Mozart did not apply the golden section to his piano sonatas.

In the end, we may never know if Mozart composed his sonatas, even in part, from equations. "We must remember," Putz writes, "that these sonatas are the work of a genius, and one who loved to play with numbers. Mozart may have known of the golden section and used it." Nevertheless, Putz thinks that the considerable variation in the data "suggests otherwise." In any case, Mozart did create divine divisions in his piano sonatas-making the interplay of sections shine like sunlight. Yet he apparently timed those divisions with his mind--not with math, or at least not with the golden section.

Originally posted by Deus ex Pianoforte: Personally, I can't wait to stop those who try to convince me of Green Day's superiority to Mozart or Beethoven in their tracks by busting out this little nugget of information. [/b]

Haha, I was playing Good Riddance on the guitar when I read this.

I heard about this equation in Mozart and other composers a few months ago. It makes sense. It's odd though, because I'm sure other composers didn't know anything about this but they subconsciously followed it. It would be interesting to check my favorite pieces of all time and see how close they come to this ratio.

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Originally posted by BruceD: I think it takes more than a piece's structure conforming to the proportions of the Golden Ratio to "prove" that classical music is superior to any other form of music.

Regards, [/b]

Agreed. Music is far more complex than even this "Golden Ratio" can be. And it's very opinionated as to what music genre/style is superior to another.

I'm surprised noone has mentionned Bartok so far - he used the series, ratio and other natural mathematical elements far far more than any other composer in history... there's a great book on the subject but the name evades me at the moment.

#363658 - 09/04/0503:17 PMRe: Proof that classical music is superior to every other genre

Skriabin
500 Post Club Member
Registered: 06/23/05
Posts: 551
Loc: li, new york

I find so often that, The rock music I used to listen to, Led Zeppelin, The beatles.

They dont have that same effect that classical does

Led zeppelin wrote songsChopin wrote beautiful Masterpieces.

The time, and effort that goes into classical burns any other type of music. Back when I played bass guitar I could learn probebly every Led Zeppelin song in a day. I could learn a Scriabin pieces in maybe a week or two.

Originally posted by BruceD: I think it takes more than a piece's structure conforming to the proportions of the Golden Ratio to "prove" that classical music is superior to any other form of music. [/b]

Well, everyone's entitled to their own opinion. :p I'm sure there's those out there that believe that Roseanne is better-looking than Anna Kournikova. But the fact is, Anna's face fits the Golden Ratio much closer than Roseanne's. Looks are based purely on math. Someone may be exclusively attracted to obese women, for whatever reason (perhaps they enjoy the feel of love handles, for example). Same thing with music. There's people out there that believe rap is superior to classical music. Even though that nature dictates that classical music is beautiful, there are those out there may claim rap is superior because it gets them "amped up for da club" so they may "get their sip on". So I suppose it all depends on what you seek in music. You seek beauty, listen to Mozart. You seek bass, listen to Ludacris.

In hindsight, I should have entitled the thread "Proof that music is inherently more beautiful than any other genre".

I believe classical music to be superior to all other musics. I tend to think of other musics as savage musics with only a beat and a simple melody line. NOt complex enough for my taste. It's only MHO though.

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"If music be the food of love, play on." -William Shakespeare

There's people out there that believe rap is superior to classical music.

Your over-simplified rage at all things modern is, quite frankly, astounding. You know, I've never met a person who claimed "rap is superior to [insert genre here]." I only hear that from people I like to call "Classicists". People are, as you say, most certainly entitled to their own opinions, which, according to you, are inherently wrong if they disagree with whatever whimsical proof you can produce.

_________________________
Every day we are afforded a new chance. The problem with life is not that you run out of chances. In the end, what you run out of are days.

Once again I find myself in agreement with Bruce although I would go further and question whether the existence of a pattern has anything to do with musical quality in general.

I feel beauty and goodness in art are extremely complicated intuitive characteristics, far too deep and convoluted to be summarised in simple numerical and statistical properties of the music.

Once a mass of data reaches a certain heft it is possible to find all sorts of orders and patterns within it. This discovery, according to what I have read, goes back at least a century to the mathematician Frank Ramsay.

Also, there is the fact that much music considered good, particularly romantic music, does not depend on form for its effect but on the semantic, intuitive qualities in isolated segments - a particular turn of melody, a certain rhythm or a poignant harmony.

Classical music may well be superior to other idioms in the eyes of many, but I find it difficult to reason that this would be the case because of a very simple numerical property.

_________________________
"It is inadvisable to decline a dinner invitation from a plump woman." - Fred Hollows

But the fact is, Anna's face fits the Golden Ratio much closer than Roseanne's.

Perhaps, but Roseanne's body fits it better than Anna's. [/b]

LOL!! Very funny, but very excellent point.

There's nothing substantial in this thread supporting classical music's superiority based on the ratio. If there is in fact occurances of this ratio in classical music that DO indeed account for its appeal, then I would put any amount of money on the fact that other styles of appealing music would also turn up occurances of the ratio, including rock. (keep in mind, that sentence started with a really big IF)

And to assert that its better because it takes longer to learn just makes no sense at all. It would be REALLY hard to learn to play chopsticks at 10 times the tempo you normally hear it, does that mean that would be a superior musical experience?

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I was born the year Glenn Gould stop playing concerts. Coincidence?

Originally posted by Derulux:Your over-simplified rage at all things modern is, quite frankly, astounding. You know, I've never met a person who claimed "rap is superior to [insert genre here]."

People are, as you say, most certainly entitled to their own opinions, which, according to you, are inherently wrong if they disagree with whatever whimsical proof you can produce. [/b]

1. I never equated rap with "all things modern". I love techno, rock, punk, and yes, even some rap. There goes that. And if you've never met a person that DOES claim rap's superiority, you need to get out more. I suggest you start with a few Philly alleyways.

2. Yes, people are entitled to their own opinions. However, we are discussing facts. Facts, by definition, are correct. Now, you can dispute that the sky is blue. But you can't disagree with its color. Know why? Cause it's a fact.

3. I didn't produce this proof. Nature did, and scientists discovered it. I just passed along the information.

Untrue, which brings me to another appearance of Phi. The ratio of your height to fingertip to fingertip (when arms are spread) plays a role in your attractiveness. How? The closer it is to the Divine Proportion.

His music can bore you all you want, but that doesn't change the fact that dozens of his works adhere to the number that makes the world go round. And you're right, listen to most rock songs and you'll see a pattern of the exact riff being used throughout the song, and with punk the same pattern exists in almost every song! They all say cops suck and booze rules.

I was once waiting for my Chinese take out and a customer walks in, sees my music books (I was on my way home from my lesson) and states, without provocation, "You know... jazz is most superior to classical music."

The guy was a jerk. I never once asked him for his opinion, and here he was pronouncing judgements!!!

No. no. no. Music does not need judgements. Whatever genre it is, it is legitimate.

It's like the coin saying "You know... heads is better than tails."

Yeeeaaaah. Like the coin would be anything without either of them!! Get real.

It's fine for heads to say "Heads are better than tails." and for tails to say "Tails are better than heads." But for the coin, heads and tails are the best!!

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"Hunger for growth will come to you in the form of a problem." -- unknown

An interesting take. I agree with you that music doesn't need judgements. All genres of music has value to someone, somewhere. All I'm saying is that even if I believed Mozart is trash, I couldn't deny that it is beautiful due to its consistency with the Universe's definition of beauty. I'm not trying to invalidate every other genre, just demonstrate how it is the only one that literally has natural beauty running through its very notes.

Originally posted by Deus ex Pianoforte:1. I never equated rap with "all things modern". I love techno, rock, punk, and yes, even some rap. There goes that. And if you've never met a person that DOES claim rap's superiority, you need to get out more. I suggest you start with a few Philly alleyways.

2. Yes, people are entitled to their own opinions. However, we are discussing facts. Facts, by definition, are correct. Now, you can dispute that the sky is blue. But you can't disagree with its color. Know why? Cause it's a fact.

3. I didn't produce this proof. Nature did, and scientists discovered it. I just passed along the information.

[/QB]

1. I don't have much to say on your first point.

2. Facts may be correct, but the conclusions that come from them are not necessarily correct. There may be many instances of that Golden Ratio in music, but as someone said earlier, with a large enough sample size you can find many patterns. Even if this isn't the case, to equate a ratio with beauty may not be correct. what makes something beautiful (or ugly) seems a bit too subjective to equate entirely on one criterion being the Golden Ratio.

3. Yes, you didn't not produce this proof, but after reading the article, i would argue that this isn't even proof in the first place. In the investigation described in the article it appears that only Mozart is investigated. What about the other classical composers? It also appears that only piano sonatas were looked at. What about piano concertos, or other types of pieces? The article also does not seem to equate the occurance of the golden ratio with superiority or beauty of the music as you did. Even the person who did the study, Putz, acknowledges the "considerable variation in tha data" so this seems far from an absolute proof. This may be considered evidence, but even so, a large variation in the data (from not a very good sample in my opinion) doesn't make this very good evidence. One might be able to draw a correlation to this and Mozart's music, but even so, only his piano sonatas as it seems that was all that was examined.

On another note, i want to disagree with your comment that the sky being blue is a fact. The sky is only sometimes blue. During a sunset for example it goes that beautiful combination of oranges and reds as well as some other colours. At night the sky is quite black.

Perhaps better evidence for Classical music being superior is the fact that it is still being played today and has been listened to longer than the musicans of todays rock, rap, techno, pop, etc music have been alive. I am sure people can agree that if something has been listened to for over 200 years, it at least can't be bad and must be good in some respects.

To look at one study that even then only looked at one composer and only one type of music and call that proof doesn't seem right. The article itself didn't even call it proof. I am not saying your hypothesis that classical music is superior to every other genre, but i wouldn't call this proof...perhaps support for the hypothesis, which can be used with other evidence to eventually form a proof.

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"There are two golden rules for an orchestra: start together and finish together. The public doesn't give a damn what goes on in between." -- Thomas Beecham

Yep. The same ratio of genders that bees use in their hives to maintain balance, is the same EXACT ratio that human faces use to attain attractiveness. That ain't a coincidence. I suppose you could attribute this definition to God, Mother Nature, the Universe or whatever your religion dictates...but humankind sure as hell didn't come up with this number.

Derekrs:

I understand your perspective and appreciate the way you disagreed with me. I did however use the sky being blue as an example. I could have easily used the grass being green instead, but that only stands true while it is alive and well (and it hasn't been painted :p ). Also, I want you to know that I used that one article as an example. When I decided to post my findings with such a controversial subject headline, I knew I would face public outcry and dissent. I googled "divine proportion Mozart" right quick so I would have an article to back my bold statements with.

This coming from someone who lives in California...or at least claims to. And where do you suppose it is that I live? I assume you've probably checked my profile, and were commenting based on that. I'd also have to presume you've lived in Philadelphia for a number of years to make that sort of comment...or are you again speaking outside your experience?

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Yes, people are entitled to their own opinions. However, we are discussing facts. Facts, by definition, are correct. Now, you can dispute that the sky is blue. But you can't disagree with its color. Know why? Cause it's a fact.

You are equating a fact to a theory. The "golden number" is a number. This is a fact. In many cases, classical music closely correlates to it. This is also a fact. Beyond that, you are interpolating. Please, do try not to confuse that, won't you?

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I didn't produce this proof. Nature did, and scientists discovered it. I just passed along the information.

You passed along an opinion, not a proof.

Bernard-[/b] Thank you. Those were beautiful words.

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I agree with you that music doesn't need judgements.

Yet, you judge....

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All I'm saying is that even if I believed Mozart is trash, I couldn't deny that it is beautiful due to its consistency with the Universe's definition of beauty.

This is an opinion, not a fact.

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The Universe's definition of beauty?

Exactly....

_________________________
Every day we are afforded a new chance. The problem with life is not that you run out of chances. In the end, what you run out of are days.

You're done. Your disrespectful and clumsy ways of twisting my words and misinterpreting my statements have worn me out. I do not feel I need to prove my home state to someone who claims to have memorized the 3rd movement of the "Moonlight" sonata in four days without a piano.

On a sidenote for the moderators, is there an ignore feature or a way of blocking members from posting on threads I've started? I'd like to continue this discussion with coherent posters.